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The NOSA-ITACA code for the modelling of the structural behaviour of historic masonry constructions

Vincenzo Binante

Maria Girardi

Cristina Padovani

Andrea Pagni

Giuseppe Pasquinelli

1

Institute of Information Sciences and

Technologies “A. Faedo”, CNR, Pisa

Science and Technology for the Safeguard of Cultural Heritage in the Mediterranean Basin Istanbul, 22nd-25th November 2011

Laboratory of Mechanics

of Materials and Structures

funded by the Region of Tuscany (PAR-FAS 2007-2013)


The NOSA-ITACA project 2011-2013

Case study

ISTI - CNR Pisa

DCR-University

of Florence

NOSA - ITACA Basic Research Consulting

Service CODE


3


The NOSA-ITACA project

NOSA-ITACA code

Case study: “Voltone”, Livorno

CONSULTING SERVICE

Municipalities

Monuments and Fine Arts Offices

Professional offices

NOSA CODE: f.e.m. nonlinear solver

SALOME: pre-post processor

4


4

The NOSA Code (http://www.isti.cnr.it/research/unit.php?unit=MMS)

•The NOSA code is a freeware finite element solver for nonlinear analyses.

•Masonry is modelled as a nonlinear isotropic elastic material with zero tensile strength and bounded compressive strength (masonry-like or no-tension material). [G. Del Piero, Meccanica 1989; S. Di Pasquale, Meccanica 1992; M.

Lucchesi, C. Padovani et al., Masonry Constructions: Mechanical Models and Numerical

Applications, Springer 2008].

• Static analyses

• Dynamic analyses

• Thermo-mechanical analyses

• Stress fields

• Collapse loads

• Elastic, fracture and crushing strain fields

• Displacement fields

• Temperature fields

• Time- histories

• NOSA library: beam, shell, plane stress, plane strain, solid and heat transfer elements (17 elements)


5


5

the infinitesimal strain tensor,

the Cauchy stress tensor,

the elastic part of the strain,

the fracture strain,

the crushing strain,

the modulus of elasticity and the Poisson’s ratio,

the masonry maximum compressive stress.

T

cE

E

fE

eE

E,

e

s0

s

00

DE

ˆ ˆT T( E ), T( E )

Given E, find Ef, Ec, T such that

e f c

f c

E = E + E + E ,

E E = 0,E

1+ν

e eT E tr( E )I ,

1 - 2

f c

0 T E T I E 0,

0

T - I 0, c

T , E 0,f

E 0

The masonry-like constitutive equation



Some example applications


• 1995 Battistero del Duomo, Volterra

• 1996 Arsenale Mediceo, Pisa

• 1998 Teatro Goldoni, Livorno

• 1998 Chiesa Madre di S. Nicolò, Noto

• 2004 Chiesa di Santa Maria Maddalena, Morano Calabro

• 2005 Chiesa di San Ponziano, Lucca

• 2008 Chiesa Abbaziale di Santa Maria della Roccella, Roccella Ionica

• 2008 Torre “Rognosa” , San Gimignano

• 2010 Torre “delle Ore”, Lucca

Sta

tic A

na

lyse

s

Dyn

am

ic A

na

lyse

s


NOSA-ITACA SOFTWARE


Until now, the NOSA solver was not supported by an efficient pre and post-processor; for this reason, the use of NOSA is limited to its developers.

One of the main aims of the NOSA-ITACA project is to develop an integrated platform, CAD/CAE software + NOSA fem code, in order to obtain a powerful tool for the safeguard of architectural heritage, available for all and flexible to upgrading.

As pre and post-processor, the SALOME platform is employed (http://www.salome-platform.org/), which is an open-source software developed by CEA ( Commissariat à l’énergie atomique et aux énergies alternatives ) and EDF industry with the support of

EURIWARE/Open Cascade.


NOSA-ITACA SOFTWARE: the Salome software as pre and post-processors


The Salome platform is based on an open and flexible architecture made of reusable components; it can be used as:

• standalone application for generation of CAD models, their preparation for numerical calculations and post-processing of the calculation results;

• alternatively, as in the NOSA-ITACA project, it can be used as a platform for integration of the external third-party fem code.

The Salome architecture was, mainly, developed in C/C++ and Python languages, which are object-oriented programming languages.


NOSA-ITACA SOFTWARE: the integration of the NOSA code


Flow-chart of integration stages NOSA-SALOME

NOSA code

Internal object

Python interface

CORBA

interface

SALOME integration

Access from CORBA/SALOME

Access outside CORBA/SALOME




What can be done with the first stage of integration

NOSA code SALOME platform

Import/Export mesh data, node and element sets

Transfer numerical results to Salome Post-Pro component

Assign to mesh items physical properties

Python interpreter

Python interface




The Salome architecture is modular, made of several components; among them, there are:

• Geometry module;

• Mesh module;

• Post-Pro module.

Each Salome module is characterized by a set of methods and attributes and specific operations can be done.

Data exchange from a Salome component to another one are done through CORBA interfaces, which each module is supplied with. The set of a Salome component and its CORBA interfaces represents a CORBA component. Each communication between a Salome module and others occurs in a CORBA server-CORBA clients way, where the CORBA server sends/receives from CORBA clients the necessary information.




According to this approach, the integration of the Nosa code in the Salome architecture must be done in the following way:

Internal object

CORBA

interface server

Corba component

CORBA bus

Client object

CORBA

interface client

Corba component

CORBA server ≡ Nosa module CORBA client ≡ Mesh or Post-Pro module




At the end of the integration process, the NOSA-ITACA software will be made of an additional module:

• Geometry module;

• Mesh module;

• Nosa module;

• Post-Pro module.

According to this integration scheme, it is possible to control locally or remotely the numerical code, from monitoring of solution progress to visualization of numerical results.


NOSA-ITACA SOFTWARE: some examples


Analysis of a vault made of masonry-like material subjected to its own weight


NOSA-ITACA SOFTWARE: some examples


Launch of NOSA solver


The “Rognosa” tower in San Gimignano

+0,00 (Square level)

+8,60 (Masonry vaults level)

+19,04 (Surrounding roofs level)

+43,34 (Top)

A A

x

z

SEZ. A-A

x

y

A

Side overlooking

the Cathedral Square

t

t




+43,34 (Top)

A A

x

z

SEZ. A-A

x

y

A

Side overlooking


t

t



The “Rognosa” tower in San Gimignano: digital acquisition of the geometry

(VC Lab – ISTI CNR)

Merging resolution=1 cm



The “Rognosa” tower in San Gimignano:

- Static analysis The Tower is subjected to its own weight and to the weight of the surrounding buildings

- Dynamic analysis The Tower subjected to the Nocera Umbra earthquake in x - direction


The “Rognosa” tower in San Gimignano: dynamic analysis




+43,34 (Top)

A A

x

z

SEZ. A-A

x

y

A

Side overlooking


t

t

Tower base section







+43,34 (Top)

A A

x

z

SEZ. A-A

x

y

A

Side overlooking


t

t




Tower vertical section




+43,34 (Top)

A A

x

z

SEZ. A-A

x

y

A

Side overlooking


t

t

The bell chamber





At time t=3,41 s: Minimum values reached during the analysis :

Compressive stress Tzz




At time t=3,41 s: Minimum values reached during the analysis :

Crushing strain Eczz




At time t=3,41 s: Maximum values reached during the analysis :

Tangential fracture strain Eftt




At time t=3,41 s: Maximum values reached during the analysis :

Fracture strain Efzz



Maximum values reached during the analysis:

Displacements ux



Conclusions

•The NOSA code is a finite element code for static and dynamic nonlinear analyses of masonry structures. The version for static analyses (COMES-NOSA) is freely downloadable at http://www.isti.cnr.it/research/unit.php?unit=MMS.

•Masonry is modelled by means of a masonry-like constitutive equation with zero tensile strength and finite or infinite compressive strength.

•The NOSA-ITACA project aims to enhance the NOSA code and disseminate the use of numerical tools in the field of maintenance and restoration of the architectural heritage.

•A case study has been presented in which the seismic vulnerability of the Rognosa Tower in San Gimignano has been assessed by means of a dynamic numerical analysis conducted via NOSA-ITACA code.

istanbul 2011

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